Which of the following substitutions should be made to evaluate the integral ∫ (4sin^2 (3x))(2cos^4 (3x))dx 4sin2 (3x) = 4 ( 1 2 - cos(6x) 2 ) and 2cos4 (3x) = 2 ( 1 2 + cos(6x) 2 ) 2 u = -cos(3x) 2cos4 (3x) = 2(1 - sin2 (3x)) 2 4sin2 (3x) = ( 1 2 - cos(3x) 2 ) and 2cos4 (3x) = - ( 1 2 + cos(3x) 2 ) 2
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Which of the following substitutions should be made to evaluate the integral ∫ (4sin^2 (3x))(2cos^4 (3x))dx 4sin2 (3x) = 4 ( 1 2 - cos(6x) 2 ) and 2cos4 (3x) = 2 ( 1 2 + cos(6x) 2 ) 2 u = -cos(3x) 2cos4 (3x) = 2(1 - sin2 (3x)) 2 4sin2 (3x) = ( 1 2 - cos(3x) 2 ) and 2cos4 (3x) = - ( 1 2 + cos(3x) 2 ) 2
![Define Q as the region bounded by the functions u(y) = y^2 / 3 + 1 and v(y) = 1 between y = 3 and y = 4. Choose the integral below that describes the volume of the solid created by rotating Q around the line x = -1. ∫3 4 π [(2)^2 - ( y^2 / 3 + 2)^2 ] dy ∫3 4 π [( y^2 / 3 ) 2 - (0)^2 ] dy ∫3 4 π [ y^2 / 3 + 1]^2 dy ∫3 4 π [( y^2 / 3 + 2)^2 - (2)^2 ] dy ∫4 3 π [( y^2 / 3 + 2)^2 - (2)^2 ] dy](https://www.doubtrix.com/uploads/editor/8220892071MUQKWoUlNW.png)